WHY DO WE NEED TO STUDY GEOMETR

Y?

WE HAVE TO STUDY GEOMETRY TO:

TO PREPARE US FOR HIGHER MATHEMATICS.

WE HAVE TO STUDY GEOMETRY TO:

UNDERSTAND AND APPRECIATE OUR NATURAL AND MAN-MADE ENVIRONMENT.

WE HAVE TO STUDY GEOMETRY TO:

PROVIDE US WITH MANY IMPORTANT FACTS OF PRACTICAL VALUE.

WE HAVE TO STUDY GEOMETRY TO:

ENHANCE OUR ANALYTICAL SKILLS TO ENABLE US TO EXPRESS OUR THOUGHTS ACCURATELY AND TRAIN US TO REASON LOGICALLY.

Before one can start to Before one can start to understand logic, and thereby understand logic, and thereby

begin to prove geometric begin to prove geometric theorems, one must first know a theorems, one must first know a

few vocabulary words and few vocabulary words and symbols.symbols.

If two angles have equal measures, then they are

congruent.

If two segments are congruent, then they have

equal measures.

1. All right angles are congruent.

If all angles are right, then they are congruent.

FOR MORE EXAMPLES: SEE PAGE 59 ,GEOMETRY TEXTBOOK

FOR MORE EXAMPLES: SEE PAGE 59 ,GEOMETRY TEXTBOOK

General Form

If p, then qp implies qp only if q

q if p

Example If x² = 4, then x = 2 x² = 4 implies x = 2x² = 4only if x = 2 x = 2 if x² = 4

If two angles have equal measures, then they are

congruent.

If two angles are congruent, then they have equal measures.

FOR MORE EXAMPLES: SEE PAGE 59 ,GEOMETRY TEXTBOOK

FOR MORE EXAMPLES: SEE PAGE 59 ,GEOMETRY TEXTBOOK

1. "If someone is a woman, then they are a human"

"If someone is a human, then they are a woman."

The converse is FALSE because a man is also a human.

The converse is FALSE because a man is also a human.

1. if r is "¬". "All men have hair,"

"All men do not have hair“

"No men have hair."

2. Sam is sleeping in class.

“ It is not true that Sam is sleeping in class”.

“Sam is not sleeping in class."

p ⇒ q read as “If p, then q”.

-p -⇒ q read as “If NOT p, then NOT q”.

Like a converse, an inverse does not necessarily have the same truth value as the original

conditional.

Like a converse, an inverse does not necessarily have the same truth value as the original

conditional.

The statement is always true with the contrapositive, but a statement is not

logically equivalent to its converse or to its inverse.

The statement is always true with the contrapositive, but a statement is not

logically equivalent to its converse or to its inverse.

If it is raining then the ground is getting wet.

If the ground is not getting wet then it is not raining.

If it is not raining then the ground is not getting wet.

If the cat will run then the dog will chase the cat.

If the dog will NOT chase the cat then the cat will NOT run.

If the cat will NOT run then the dog will NOT chase the cat.

If the dog will chase the cat then the cat will run.

“If p then q”

“If negation of p then negation of q”

“If q then p”

“If negation of q then negation of p”

NOTE: The conditional statement and its contra positive are logically equivalent

"If and only if p, then q" means both that p implies q and that q

implies p.

"If and only if p, then q" means both that p implies q and that q

implies p.

1. p Mom plays the guitar.

q Dad plays the piano.p ∧ q

" Mom plays the guitar and Dad plays the piano ."

1. p Mom plays the guitar.

q Dad plays the piano.p V q

" Mom plays the guitar or Dad plays the piano ."

1. It is a square or it is a trapezoid.

It is not a square.

It is a trapezoid.

Get one-half crosswise

Given the conditional statement, state the inverse, converse and its contra positive.

“If today is Tuesday then tomorrow is Wednesday”

Suppose p stands for “Hawks swoop” and q stands for “Gulls glide”.

Express the following in symbolic form each of the following statements.

1. Hawks swoop or gulls glide. 2. Gulls do not glide.3. Hawks do not swoop or gulls do not glide.

4. Hawks do not swoop and gulls do not glide.

Let’s see if your

answers are

correct.

“If today is Tuesday then tomorrow is Wednesday”

“If today is not Tuesday then tomorrow is not Wednesday”

“If tomorrow is Wednesday then today is Tuesday ”

“If tomorrow is not Wednesday then today is not Tuesday ”

Suppose p stands for “Hawks swoop” and q stands for “Gulls glide”.

Express the following in symbolic form each of the following statements.

1. Hawks swoop or gulls glide. 2. Gulls do not glide.3. Hawks do not swoop or gulls do not glide.

4. Hawks do not swoop and gulls do not glide.

p V q

q

p V q

p Ʌ q

Perfect score is 7.Pass your

paper.

 

Inductive Versus Deductive Reasoning